Another critique is that one cannot express natural data-dependent assumptions through the PAC framework. For instance, high-dimensional data may lie in a low-dimensional manifold. To be more specific, consider the task of classifying images of vehicles. The representation of such images corresponds to a low-dimensional subset of the space of all possible images, most of which do not correspond to vehicles.
A prominent way to capture such assumptions is via partial concepts [1]}: these are functions which can be undefined on a subset of \(\mathcal {X}\) , a departure from the traditional model.
